The coming weeks could be crucial for Herbalife, one of America's fastest-growing companies. The nutrition-supplement powerhouse is facing allegations that its business model is really a get-rich-quick scheme. In just over three decades, Herbalife has gone from struggling startup to $5 billion in annual sales worldwide. So how has it rivaled some century-old mainstays?

Activist investor Bill Ackman's answer during a three-hour attack on the company last month sent the stock into a tailspin.

"Herbalife is a pyramid scheme," Ackman declared. He asked how a company that does virtually no advertising can sell so much of its "Formula 1" weight-loss powder. Its sales numbers come close to matching Oreos, Ackman points out, and outrank such household names as Palmolive and Clorox.

"You think about the dominance of those brands, it's remarkable," Ackman said. "The only $2 billion brand, we say, that nobody's ever heard of."

Ackman claims Herbalife makes its money from buyers at the top of what he calls a "pyramid," recruiting distributors who buy products and recruit more distributors, all in hopes of big rewards. CEO Michael Johnson -- who by some accounts was the highest-paid executive in America last year -- wasted no time delivering an angry response on CNBC.

"We're not a pyramid scheme," said Johnson. "That's a bogus accusation."